MobLab
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Aa

Ascending Clock Auction

Game Description

Each bidder has a randomly determined private value for one unit of a good. The auction price ticks up at regular intervals, and a bidder can drop out at any time. The auction ends when the number of remaining bidders equals the number of items. Each of these remaining bidders receives one item, and pays the ending price.

Learning Objective 1: Ascending Clock Auctions

Demonstrates the workings of an ascending clock auction.

Learning Objective 2: Nash Equilibrium Bid Function

The payoff maximizing strategy for each bidder is to leave the auction when the current price is equal to her value.

Learning Objective 3: Relationship to Other Types of Auctions

Play this game in conjunction with the descending clock auction, or the first-price sealed-bid auction, to show the difference in optimal bidding strategies. You can also show that the optimal bidding strategy in the ascending clock is similar to that of the private-value second-price sealed bid auction.

Brief Instructions

By default, the auction price starts at $0 (Start Price), and increases by $5 (Price Increment) every 2 seconds (Increment Duration). Each bidder values one unit, and this value is drawn from the uniform distribution from Lowest Bidder Value=$10 to Highest Bidder Value=$100. Each bidder draws a new value for each new period if multiple rounds are specified (Periods> 1). Each player has a weakly dominant strategy to exit at the highest price that does not exceed her value.

Note: In order to make sure that this strategy entails exiting when the auction price exactly equals the player’s value, make sure Start Price is a multiple of Price Increment, and less than or equal to Lowest Bidder Value (e.g. $0). This is because bidder values are rounded in increments of Price Increment. Thus, if Price Increment=$7, Lowest Bidder Value=$10 and Highest Bidder Value=$100, bidder values will be randomly chosen from {$14, $21,..., $91, $98}. With Start Price=$0, price increments will be {$0, $7, $14,..., $91, $98}.

Key Treatment Variations

With Units > 1, multiple units are on auction, but each bidder still values one unit. The auction ends when Remaining Bidders = Units. Each winner pays the a price equal to the Current Price at auction end.

Results

The results highlight the Nash Equilibrium and show how close your students were to equilibrium play. Use the Go To: menu to switch between periods.

Figure 1: Outcome Summary Table. (Click to expand)

For each round, there is a table summarizing each group’s performance (Figure 1). With Units = X, the first columns display the sum of the X-highest item values (Optimal Surplus) and the sum of the winners’ item values (Surplus).1 The final column shows seller Revenue (winning price × X). Check the radio button to reveal a figure summarizing a group’s bidding.

Figure 2: Participant Bids and Values. (Click to expand)

By unchecking the first two check-boxes for the Nash Equilibrium Bid Function and Best Fit Line, only markers that indicate the exit price and bidder value for each participant remain (Figure 2). If a player did not exit during the auction, her value is not plotted.

Figure 3: Nash Equilibrium Bid Function and Best Fit Line

The equilibrium strategy in this auction is to exit (bid) when Current Price=Bidder's Value. To compare participant results with the optimal strategy, use the Nash Equilibrium bid function and best fit line. With the Nash Equilibrium Bid Function box checked, the Exit Price = Bidder's Value line is plotted. With the Best Fit Line box checked, a linear trend line is fitted to bidder exit prices and values (Figure 3). This line will coincide with the Bid Function if all students played equilibrium strategies.

Robot Play

Our robot (i.e., an automated player) strategy is the following:

Robots leave the auction as soon as the price equals their value.

1. Surplus calculations assume the items have no value to the seller.
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